Math Chapter Wise

EnglishUP PCS (Pre) 1994

Q261.The value of / 2 0 cosx dx 1 sinx is–

A/ 2 0 cos x dx 1 cos x B/ 2 0 sin x dx 1 sin x C/ 2 0 sin x dx 1 cos x Dnone of these

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EnglishUP PCS (Pre) 1994

Q262.2 2 a x 0 e dx is equal to–

AImage/formula option A (see source) B/ 2a C/ 4a D2a

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EnglishUP PCS (Pre) 1995

Q263./ 2 3 / 2 (sin x) dx is equal to–

A0 Bcos π2 C2 cos π3 DThe value does not exist

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EnglishUP PCS (Pre) 1995

Q264.The value of 0 (sinx)dx π ∫ ∫ xf is–

A0 (sin x)dx π ∫ f B0 sin x dx 2 π ∫ f C() 0 sin x dx 2 π ∫ f D/ 2 0 sin x dx f

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EnglishUP PCS (Pre) 1995

Q265.The value of the integral 1 1 2 2 0 0 (x y)dx.dy + ∫∫ ∫∫ is–

A1 B0 C1/3 D2/3

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EnglishUP PCS (Pre) 1995

Q266.The value of integral 1 3 2 1 x dx 1 x is–

A2 B2/3 C0 D1

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EnglishUP PCS (Pre) 1996

Q267.If / 2 n n 0 U sin d, n 1, then the value of n n 2 n 1 U U n is–

A2 1 n 1 B1/(n 1) C2 1 n DNone of these

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EnglishUP PCS (Pre) 1996

Q268.The ratio of the area bounded by the curve a4 y2 = x5 (2a – x) and that of the circle of radius a, is:

A2: 3 B5: 4 C4: 5 DNone of these

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EnglishUP PCS (Pre) 1996

Q269.The value of ∫ n-1 m +n 0 x dx (1 + x) ∞ is:

AГ(m)Г(n)/2Г(m + n) BГ(m)Г(n)/Г(m + n) CГ(m)Г(n)/Г(m + n +1) DNone of these

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EnglishUP PCS (Pre) 1999

Q270.The value of integral ∫ 3 1 2 2 -1 x dx (x + 2)

Alog 3 B0 C1/9 D2/9

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EnglishUP PCS (Pre) 1999

Q271.The vaue of () ∫ π/2 0 cos x -sin x dx 1+ sin x cos x is:

A1 B1/2 C0 D2

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EnglishUP PCS (Pre) 1999

Q272.∫ 1 2 0 log(1+x) dx 1+x is equal to:

Alog2 4 π Blog2 8 π Clog2 7 π D8/π

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EnglishUP PCS (Pre) 1999

Q273.1 ∞ →∞ ∫ -x u dx lim 1+ e equals:

A∞ B1 C0 Dlog(e+1)

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EnglishUP PCS (Pre) 1999

Q274.The value of the double integral 2 − ∫ ∫ x 0 (sinx)y dx dy: is

A32 B16 C4 D0

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EnglishUP PCS (Pre) 1999

Q275.The value of the integral ∫∫xy dx dy taken over the region bounded by the two axes and the straight line x+y = 1

A1/20 B1/24 C1/30 D1/40

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EnglishUP PCS (Pre) 2000

Q276.If (((()))) ((()) n a 2 2 n 0 I a x dx, n 0 = − > = − > = − > = − > ∫ ∫ then the value of I3 is:

A4 24 a 35 B7 24 a 35 C4 16 a 35 D7 16 a 35

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EnglishUP PCS (Pre) 2000

Q277.The value of the double integral (((()))) 2 2 x y dxdy + ∫∫ ∫∫ over the region in the positive quadrant for which x + y ≤ 1 is:

A1/3 B1/12 C1/6 D1/4

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EnglishUP PCS (Pre) 2000

Q278.If n 4 n 0 tan xdx π φ = φ = ∫ ∫ ∫, then n n 2 − φ + φ + φ + φ + φ is equal to:

A1/n B−1/n 1 C−n/n 1 D−n 1/n

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EnglishUP PCS (Pre) 2000

Q279.The value of the integral 1 | x |dx − ∫ ∫ is equal to:

A0 B1/2 C1 D2

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EnglishUP PCS (Pre) 2000

Q280.The value of the integral 2 0 dx 1 tan x π + ∫ ∫ is:

Aπ Bπ/3 Cπ/2 Dπ/4

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